Make a spherical background image
This is similar to the question asked here: How can an equidistance, spherical panorama image be generated from Blender Cycles? See the answer for information on setting up a Cycles-based equirectangular camera.

As Leander mentioned: If you prefer to use Blender Internal or the Blender Game Engine, a Skybox is probably your best bet (simply render six 90º FOV square images, then make a cube out of the results and use that to surround your scene.